Tohoku Mathematical Journal
2018
December
SECOND SERIES VOL. 70, NO. 4

Tohoku Math. J.
70 (2018), 511-521

Title ON THE K-STABILITY OF FANO VARIETIES AND ANTICANONICAL DIVISORS

Author Kento Fujita and Yuji Odaka

(Received February 22, 2016, revised June 23, 2016)
Abstract. We apply a recent theorem of Li and the first author to give some criteria for the K-stability of Fano varieties in terms of anticanonical $\mathbb{Q}$-divisors. First, we propose a condition in terms of certain anti-canonical $\mathbb{Q}$-divisors of given Fano variety, which we conjecture to be equivalent to the K-stability. We prove that it is at least a sufficient condition and also related to the Berman-Gibbs stability. We also give another algebraic proof of the K-stability of Fano varieties which satisfy Tian's alpha invariants condition.

Mathematics Subject Classification. Primary 14J45; Secondary 14L24.
Key words and phrases. Fano varieties, K-stability, Kähler-Einstein metrics.

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